TSTP Solution File: FLD060-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD060-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 22:27:43 EDT 2023
% Result : Unsatisfiable 0.93s 1.01s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 20
% Syntax : Number of formulae : 40 ( 15 unt; 12 typ; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 25 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
sum: ( $i * $i * $i ) > $o ).
tff(decl_23,type,
additive_identity: $i ).
tff(decl_24,type,
defined: $i > $o ).
tff(decl_25,type,
additive_inverse: $i > $i ).
tff(decl_26,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
multiplicative_identity: $i ).
tff(decl_28,type,
multiplicative_inverse: $i > $i ).
tff(decl_29,type,
add: ( $i * $i ) > $i ).
tff(decl_30,type,
multiply: ( $i * $i ) > $i ).
tff(decl_31,type,
less_or_equal: ( $i * $i ) > $o ).
tff(decl_32,type,
a: $i ).
tff(decl_33,type,
b: $i ).
cnf(totality_of_addition,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(less_or_equal_3,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_3) ).
cnf(transitivity_of_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',transitivity_of_order_relation) ).
cnf(not_less_or_equal_4,negated_conjecture,
~ less_or_equal(add(a,a),add(b,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_4) ).
cnf(c_0_8,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_addition ).
cnf(c_0_9,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_10,hypothesis,
( sum(X1,b,add(X1,b))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_12,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
compatibility_of_order_relation_and_addition ).
cnf(c_0_13,hypothesis,
sum(b,b,add(b,b)),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_14,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_15,hypothesis,
sum(a,b,add(a,b)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,hypothesis,
( less_or_equal(X1,add(b,b))
| ~ less_or_equal(X2,b)
| ~ sum(X2,b,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
less_or_equal(a,b),
less_or_equal_3 ).
cnf(c_0_18,hypothesis,
sum(b,a,add(a,b)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,hypothesis,
( sum(X1,a,add(X1,a))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_20,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation ).
cnf(c_0_21,hypothesis,
less_or_equal(add(a,b),add(b,b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_15]),c_0_17])]) ).
cnf(c_0_22,hypothesis,
( less_or_equal(X1,add(a,b))
| ~ less_or_equal(X2,b)
| ~ sum(X2,a,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_23,hypothesis,
sum(a,a,add(a,a)),
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_24,negated_conjecture,
~ less_or_equal(add(a,a),add(b,b)),
not_less_or_equal_4 ).
cnf(c_0_25,hypothesis,
( less_or_equal(X1,add(b,b))
| ~ less_or_equal(X1,add(a,b)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,hypothesis,
less_or_equal(add(a,a),add(a,b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_17])]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD060-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.34 % Computer : n002.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Aug 27 23:46:19 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.93/1.01 % Version : CSE_E---1.5
% 0.93/1.01 % Problem : theBenchmark.p
% 0.93/1.01 % Proof found
% 0.93/1.01 % SZS status Theorem for theBenchmark.p
% 0.93/1.01 % SZS output start Proof
% See solution above
% 0.93/1.02 % Total time : 0.433000 s
% 0.93/1.02 % SZS output end Proof
% 0.93/1.02 % Total time : 0.436000 s
%------------------------------------------------------------------------------